On Bayesian Posterior Mean Estimators in Imaging Sciences and Hamilton–Jacobi Partial Differential Equations

Variational and Bayesian methods are two widely used set of approaches to solve image denoising problems. In a setting, these correspond, respectively, using maximum posteriori estimators posterior mean for reconstructing images. this paper, we propose novel theoretical connections between Hamilton–Jacobi partial differential equations (HJ PDEs) broad class with quadratic data fidelity term log-concave prior. Where solutions some first-order HJ PDEs initial describe estimators, here show that viscous estimators. We use establish representation formulas various properties particular, can be expressed as proximal mappings smooth functions derive functions.